1. The two main classes of hyperbolic dynamical systems for which an active use of computer techniques is planned are as follows. a. Non-uniformly hyperbolic dynamics. For these models the finer details of the statistical properties are hard to tell. The exact rate of correlation decay is only understood in some exceptional cases that possess special symmetries; a problem to which simulations can easily provide an appropriate approach. b. Dynamics with mixed phase space structure. For such systems long time behavior is characterized both by stable and by chaotic phenomena. It is to be studied numerically how the phase space structure changes, how ergodicity is destroyed by the appearance of islands when a continuous parameter is altered in certain two dimensional models. In the multidimensional case, among others, the issue of ergodicity versus islands for hard ball systems in different types of containers is to be investigated.2. In the field of information theory quantum methods seem to be very promising recently. Clarifying the role of fidelity, the mostly used distortion measure is a main goal of the project.3. Studying reaction diffusion systems our aim is to numerically solve their deterministic models, to simulate their different stochastic models, and also to do qualtiative investigations.4. In the field of computer algebra:a. We try to find construction algorithms for the computations and also to study both the theory and application of Gröbner basis of finite point sets. b. We plan to do research in the field of factorization of polynomials and their application in computer algebra and primality testing. We would like to implement and use fast polynomial arithmetics and factorization programs. c. Within the present work we plan to develop parts of mathematical program packages such as Mathematica and Maple, based upon our theoretical results.

Main objective of our proposal was to open up radically new perspectives for the extensive and colourful activity in the field of computationally sensitive research performed at the Institute of Mathematics of BME. Special emphasis was put on the participation of (both undergraduate and graduate) students of our Institute in this type of mathematical research. The intensive contribution of skilfull students played a principal role in our success; we managed to increase the level of our computationally sensitive research activity with several orders of magnitude during the years of OTKA support. Not aiming for completeness, some of the most interesting results are mentioned below (for more information see the detailed research report):
- Hyperbolic dynamical systems and statistical physics: estimating the Hausdorff measure of known fractals, investigation of random walks with internal states, issue of feedback stabilization of unstable linear oscillators.
- Quantum information theory: estimating the state of quantum systems, related matrix-search problems in the algebra of 4 by 4 matrices.
- Computer algebra and related fields: Gröbner bases and their relation to combinatorics, global properties of zero dimensional polinom ideals, computer-aided study of S-extremal set systems.
- Reaction-diffusion equations: estimating parameters eg. for systems with detailed balance, mobility management algorithms, approximate solutions, sensitivity analysis.